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81.
Enrique Bendito ngeles Carmona Andr s M. Encinas 《Applied Numerical Mathematics》2004,50(3-4):343-370
Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form
for suitable choices of q,
and
. In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q,
and
. 相似文献
82.
Dominique Tourns 《Historia Mathematica》2003,30(4):457
In the period which precedes the appearance of computers, needs in calculation of the scientists and engineers led to an important development of graphic methods of integration. To contribute to the study of this little known phenomenon, the article presents techniques and instruments used for the graphic integration of ordinary differential equations, and looks for their historic origins by going back to the beginning of calculus: processes of geometric calculation by the polygonal method or the method of radius of curvature, use of tractional motion for the conception of integraphs, reduction to graphic quadratures in finite or infinite number. 相似文献
83.
Inés CarrancoJosé Luis D?&#x;az Oscar JiménezRodolfo Lavilla 《Tetrahedron letters》2003,44(46):8449-8452
The Lewis acid-catalyzed interaction of dihydropyridines with ethyl glyoxalate and primary aliphatic amines yields, depending on the reaction conditions, bicyclic aminals or rearranged tetrahydropyridines in one-pot multicomponent reactions. 相似文献
84.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
85.
The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed. 相似文献
86.
87.
Francisco Jesús Castro-Jiménez José Marı́a Ucha-Enrı́quez 《Comptes Rendus Mathematique》2004,338(6):461-466
We prove a duality theorem for some logarithmic -modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case. To cite this article: F.J. Castro-Jiménez, J.M. Ucha-Enr??quez, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
88.
Richard Arratia Bla Bollobs Gregory B. Sorkin 《Journal of Combinatorial Theory, Series B》2004,92(2):199-233
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers. 相似文献
89.
90.
Stereoselectivity in the intermolecular Pauson-Khand reaction of electron-deficient terminal alkynes
A family of terminal alkyne dicobalthexacarbonyl complexes bearing groups with a range of electron-withdrawing abilities has been synthesized. After submitting these complexes to the intermolecular Pauson-Khand reaction with norbornadiene, electron-deficient substrates afforded up to 26% of the unexpected endo-cyclopentenone. 相似文献